The 20-year-old, who will stay with the club until January 4, came through the ranks with the Shrews and has made 18 appearances for the League One side this season, including 90 minutes in their midweek loss to Oldham.
"Connor is a very good defender," manager Mark Yates told the club's official website.
"He is big, strong and mobile. We are lacking in numbers in defence so he will certainly bolster our options."
The Robins also signed Bristol City winger Toby Ajala on Thursday to boost Yates' options ahead of the trip to Southend.